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On Large Games with a Bio-Social Typology

Author

Listed:
  • M. Ali Khan
  • Kali P. Rath
  • Yeneng Sun
  • Haomiao Yu

Abstract

We present a comprehensive theory of large non-anonymous games in which agents have a name and a determinate social-type and/or biological trait to resolve the dissonance of a (matching-pennies type) game with an exact pure-strategy Nash equilibrium with finite agents, but without one when modeled on the Lebesgue unit interval. We (i) establish saturated player spaces as both necessary and sufficient for an existence result for Nash equilibrium in pure strategies, (ii) clarify the relationship between pure, mixed and behavioral strategies via the exact law of large numbers in a framework of Fubini extension, (iii) illustrate corresponding asymptotic results.

Suggested Citation

  • M. Ali Khan & Kali P. Rath & Yeneng Sun & Haomiao Yu, 2011. "On Large Games with a Bio-Social Typology," Economics Working Paper Archive 585, The Johns Hopkins University,Department of Economics.
    • Handle: RePEc:jhu:papers:585
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    1. Podczeck, Konrad, 2008. "On the convexity and compactness of the integral of a Banach space valued correspondence," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 836-852, July.
    2. M Ali Khan & Kali P Rath & Yeneng Sun, 1998. "Pure-Strategy Nash Equilibrium Points in Large Non-Anonymous Games," Economics Working Paper Archive 393, The Johns Hopkins University,Department of Economics.
    3. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    4. Roger Guesnerie & Pedro Jara-Moroni, 2011. "Expectational coordination in simple economic contexts," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 47(2), pages 205-246, June.
    5. Jianwei Wang & Yongchao Zhang, 2012. "Purification, saturation and the exact law of large numbers," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(3), pages 527-545, August.
    6. Carmona, Guilherme & Podczeck, Konrad, 2009. "On the existence of pure-strategy equilibria in large games," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1300-1319, May.
    7. Edward Cartwright & Myrna Wooders, 2009. "On purification of equilibrium in Bayesian games and expost Nash equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(1), pages 127-136, March.
    8. George A. Akerlof & Rachel E. Kranton, 2000. "Economics and Identity," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 115(3), pages 715-753.
    9. William A. Brock & Steven N. Durlauf, 2001. "Discrete Choice with Social Interactions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(2), pages 235-260.
    10. Khan, M. Ali & Yeneng, Sun, 1995. "Pure strategies in games with private information," Journal of Mathematical Economics, Elsevier, vol. 24(7), pages 633-653.
    11. Rath, Kali P. & Yeneng Sun & Shinji Yamashige, 1995. "The nonexistence of symmetric equilibria in anonymous games with compact action spaces," Journal of Mathematical Economics, Elsevier, vol. 24(4), pages 331-346.
    12. Robert J. Aumann & Jacques H. Dreze, 2008. "Rational Expectations in Games," American Economic Review, American Economic Association, vol. 98(1), pages 72-86, March.
    13. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    14. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    15. George A. Akerlof & Rachel E. Kranton, 2002. "Identity and Schooling: Some Lessons for the Economics of Education," Journal of Economic Literature, American Economic Association, vol. 40(4), pages 1167-1201, December.
    16. M. Khan & Kali Rath & Yeneng Sun, 2006. "The Dvoretzky-Wald-Wolfowitz theorem and purification in atomless finite-action games," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(1), pages 91-104, April.
    17. Khan, M. Ali & Sun, Yeneng, 2002. "Non-cooperative games with many players," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 46, pages 1761-1808, Elsevier.
    18. Mas-Colell, Andreu, 1984. "On a theorem of Schmeidler," Journal of Mathematical Economics, Elsevier, vol. 13(3), pages 201-206, December.
    19. Peter J. Hammond & Yeneng Sun, 2003. "Monte Carlo simulation of macroeconomic risk with a continuum of agents: the symmetric case," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(2), pages 743-766, March.
    20. Khan, M. Ali & Sun, Yeneng, 1999. "Non-cooperative games on hyperfinite Loeb spaces1," Journal of Mathematical Economics, Elsevier, vol. 31(4), pages 455-492, May.
    21. Yeneng Sun, 1999. "The complete removal of individual uncertainty: multiple optimal choices and random exchange economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(3), pages 507-544.
    22. Blume, Lawrence E. & Brock, William A. & Durlauf, Steven N. & Ioannides, Yannis M., 2010. "Identification of Social Interactions," Economics Series 260, Institute for Advanced Studies.
    23. Anderson, Robert M., 1992. "The core in perfectly competitive economies," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 14, pages 413-457, Elsevier.
    24. Rui Pascoa, Mario, 1993. "Approximate equilibrium in pure strategies for non-atomic games," Journal of Mathematical Economics, Elsevier, vol. 22(3), pages 223-241.
    25. George-Marios Angeletos & Christian Hellwig & Alessandro Pavan, 2007. "Dynamic Global Games of Regime Change: Learning, Multiplicity, and the Timing of Attacks," Econometrica, Econometric Society, vol. 75(3), pages 711-756, May.
    26. Konrad Podczeck, 2010. "On existence of rich Fubini extensions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 1-22, October.
    27. Sun, Yeneng, 2006. "The exact law of large numbers via Fubini extension and characterization of insurable risks," Journal of Economic Theory, Elsevier, vol. 126(1), pages 31-69, January.
    28. Paul R. Milgrom & Robert J. Weber, 1985. "Distributional Strategies for Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 619-632, November.
    29. Richard McLean & Andrew Postlewaite, 2002. "Informational Size and Incentive Compatibility," Econometrica, Econometric Society, vol. 70(6), pages 2421-2453, November.
    30. Steven N. Durlauf & Yannis M. Ioannides, 2010. "Social Interactions," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 451-478, September.
    31. Yu, Haomiao & Zhang, Zhixiang, 2007. "Pure strategy equilibria in games with countable actions," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 192-200, February.
    32. Rashid, Salim, 1983. "Equilibrium points of non-atomic games : Asymptotic results," Economics Letters, Elsevier, vol. 12(1), pages 7-10.
    33. Ehud Kalai, 2004. "Large Robust Games," Econometrica, Econometric Society, vol. 72(6), pages 1631-1665, November.
    34. Roberts, Donald John & Postlewaite, Andrew, 1976. "The Incentives for Price-Taking Behavior in Large Exchange Economies," Econometrica, Econometric Society, vol. 44(1), pages 115-127, January.
    35. Sun, Yeneng & Zhang, Yongchao, 2009. "Individual risk and Lebesgue extension without aggregate uncertainty," Journal of Economic Theory, Elsevier, vol. 144(1), pages 432-443, January.
    36. Roy Radner & Robert W. Rosenthal, 1982. "Private Information and Pure-Strategy Equilibria," Mathematics of Operations Research, INFORMS, vol. 7(3), pages 401-409, August.
    37. Cremer, Jacques & McLean, Richard P, 1985. "Optimal Selling Strategies under Uncertainty for a Discriminating Monopolist When Demands Are Interdependent," Econometrica, Econometric Society, vol. 53(2), pages 345-361, March.
    38. Rath, Kali P., 1996. "Existence and upper hemicontinuity of equilibrium distributions of anonymous games with discontinuous payoffs," Journal of Mathematical Economics, Elsevier, vol. 26(3), pages 305-324.
    39. William A. Brock & Steven N. Durlauf, 2010. "Adoption Curves and Social Interactions," Journal of the European Economic Association, MIT Press, vol. 8(1), pages 232-251, March.
    40. Carmona, Guilherme, 2008. "Large games with countable characteristics," Journal of Mathematical Economics, Elsevier, vol. 44(3-4), pages 344-347, February.
    41. David Housman, 1988. "Infinite Player Noncooperative Games and the Continuity of the Nash Equilibrium Correspondence," Mathematics of Operations Research, INFORMS, vol. 13(3), pages 488-496, August.
    42. Mario Rui Pascoa, 1998. "Nash equilibrium and the law of large numbers," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(1), pages 83-92.
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    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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